Question

Solve the equation -
2+5+8+..........+x=155.

Answer 1

GIVEN :-

First Term is (a) = 2

Common difference (d)= 3

sum of x terms Sx = 155

TO FIND :- x

SOLUTION :-

Sx = x/2 [ 2a + (x -1)d ]       {FORMULA}

=> 155 = x/2 [ 2 * 2 + (x - 1) 3]

=> 155 = x/2 [ 4 + 3x - 3]

=> 155 = x/2 [ 1 + 3x ]

=> 155 = (x + 3x^2)/2

=> 310 = 3x^2 + x

=> 3x^2 + x - 310 = 0

Now we shall solve this equation by discriminant formula,

Here a = 3 , b = 1 and c = - 310

d = b^2 - 4ac

= 1 - 4 * 3 * - 310

= 1 + 3720

= 3721

$x =\frac{ - b +  - \sqrt{d}}{2a}$

x =( -1 + 61)/2*2   or   x =( -1-61)/2*2

=> 60/4                or      -62/4

=> 15                   or       - 15.5

But x = - 15.5 is not possible .

Therefore, x = 15